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NCERT Solutions for Class 6 Maths Chapter 11 Algebra are discussed in this article. These NCERT solutions are created by expert team at careers360 considering the latest CBSE syllabus 2023. This is a very important branch of mathematics comprising 5 exercises and 27 questions. You will get NCERT Class 6 Maths solutions of chapter 11 for these all questions. In this NCERT solutions for Algebra class 6 Maths chapter 11, you will study algebraic expressions. This chapter of NCERT will give you some basics of algebra. These CBSE NCERT solutions for Class 6 Maths chapter 11 algebra are very useful in solving many reallife problems using variables.
There are many questions in solutions of NCERT for Class 6 Maths chapter 11 algebra where you will learn to form an equation and solve them. Apart from that, there are some practice questions given at the end of every topic for conceptual clarity. NCERT Solutions for Class 6 are prepared by expert faculty to clear doubts which will aid you to understand the concepts given in NCERT 6 Class Maths Syllabus. Scroll down to access NCERT solutions for Class 6 Maths chapter 11. Also, Check NCERT Solutions to get class 6 to 12 solutions for Science and Maths. Understanding the concept of variables and equations are mandatory for our higher studies. So solving all the NCERT questions are mandatory. Solve as many questions as possible from this chapter.
literal numbers or literals = Letters to represent numbers
Commutative property of addition, a + b = b + a, where variables a and b can represent any number.
Consider two literal numbers x and y
x∗y = xy
5∗x = 5x
x∗3 = 3x
a∗a∗.............∗a (12 times ) = a^{12}
In expressions like this x^{9}, the number 9 is called the index or exponent, and the letter x is called the base.
Constant = Same numerical value
Patterns using matchsticks: Exploring the arrangement of matchsticks to create letters and shapes, identifying the number of matchsticks required for repeating a given shape.
Variable: A symbol or letter (e.g., n) that represents a quantity or value that can vary or change. The value of a variable is not fixed and can take on different values.
Fixed value: Some quantities, like the number of angles in a triangle, have a specific and unchanging value. They are not variables.
Expressing relations: Variables allow us to express relationships and connections between quantities in various practical situations.
Operations on variables: Variables can be manipulated using operations such as addition, subtraction, multiplication, and division, similar to fixed numbers. Expressions involving variables can be formed, such as x  3, x + 3, 2n, 5m, 3p, 2y + 3, 3l  5, etc.
General rules: Variables enable us to express general rules and principles in both geometry and arithmetic. For example, the
Equation: A mathematical statement that equates two expressions or quantities. It states that the expression on the lefthand side (LHS) is equal to the expression on the righthand side (RHS), using the equal (=) sign. For example, x  3 = 10 is an equation.
LHS and RHS: An equation has two sides, the lefthand side (LHS) and the righthand side (RHS), with the equal (=) sign in between.
Solution of an equation: The specific value(s) of the variable that satisfy the equation, making both the LHS and RHS of the equation equal. These values are called the solutions of the equation.
Trial and error method: A method for finding the solution(s) of an equation by systematically trying different values for the variable and checking if they satisfy the equation. Different values are tested until the correct value that satisfies the equation is found.
Free Download NCERT Solutions for Class 6 Maths Chapter 11 Algebra For CBSE Exam
(a) A pattern of letter T as .
(b) A pattern of letter Z as .
(c) A pattern of letter U as .
(d) A pattern of letter V as .
(e) A pattern of letter E as .
(f) A pattern of letter S as .
(g) A pattern of letter A as .
Answer:
(a) A pattern of letter T as ( because 2 matchsticks are used )
(b) A pattern of letter Z as ( because 3 matchsticks are used )
(c) A pattern of letter U as ( because 3 matchsticks are used )
(d) A pattern of letter V as ( because 2 matchsticks are used )
(e) A pattern of letter E as ( because 5 matchsticks are used )
(f) A pattern of letter S as ( because 5 matchsticks are used )
(g) A pattern of letter A as ( because 6 matchsticks are used )
Answer: Letter "T" and "v" has pattern 2n because 2 matchsticks are used in these two letters.
Answer: Cadets in a row = 5
number of rows = n
Thus, the total number of cadets = 5n
Answer: Mangoes in a box = 50
Number of boxes = b
Thus, the total number of mangoes = 50b
Answer: pencils per student = 5
number of students = s
Thus, the total pencils needed = 5s
Answer: Time taken by bird = t minutes
Speed of bird = 1 km per minute
Thus, distance covered by bird
Answer: Number of rows = r
Number of dots in each row = 9 dots
Thus, the total number of dots = 9r
When the number of rows is 8, then the total number of dots are dots.
When the number of rows is 10, then the total number of dots are dots.
Answer: Radha's age = x years
Thus, age of Leela = (x4) years
Answer: Number of laddus given = l
Number of laddus remaining = 5
Thus,tota number of laddus = (l+5)
Answer: Number of oranges in one box = x
Number of box = 2
So, the total number of oranges = 2x
Remaining number of oranges = 10
Thus, the number of oranges = 2x+10
Answer:
(a) 4 matchsticks
(b) 7 matchsticks
(c) 10 matchsticks
(d) 13 matchsticks
If we remove 1 matchstick from each then it forms a table of 3 i.e.,3,6,9,12,.....
So, required equation = 3x+1 , x= number of squares
Answer:
(a) 3 matchsticks
(b) 5 matchsticks
(c) 7 matchsticks
(d) 9 matchsticks
If we remove 1 matchstick from each then it forms a table of 2 i.e., 2,4,6,8............
So, required equation = 2x+1 , x= number of triangles
Question: 1 The side of an equilateral triangle is shown by . Express the perimeter of the equilateral triangle using
Answer: The side of an equilateral triangle is .
Therefore, the perimeter of the equilateral triangle
Answer: The side of a hexagon is l.
Therefore, the perimeter of the hexagon
Answer: Length of one edge of cube = l
Number of edges in a cube = 12
So, total length =
Answer: Length of diameter is double the length of the radius.
Thus,d = 2r
Question: 5 To find sum of three numbers and we can have two ways:
(a) We may first add and to get and then add to it to get the total sum or
(b) We may add and to get and then add to get the sum Thus,
This can be done for any three numbers. This property is known as the associativity of addition of numbers. Express this property which we have already studied in the chapter on Whole Numbers, in a general way, by using variables a, b and c.
Answer: According to the given condition,
Answer: The other expressions are :
(i)
Question: 2 Which out of the following are expressions with numbers only?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Answer: Option (c) and (d) are with numbers only. All other expression contains alphabets
(a)
(b)
(c)
(d)
Answer:
(a)
(b)
(c)
(d)
Question: 4(i) Give expressions for the following cases.
(a) added to
(b) subtracted from
(c) multiplied by
(d) divided by
(e) subtracted from
(f) multiplied by
(g) divided by
(h) multiplied by
Answer:
(a) added to
(b) subtracted from
(c) multiplied by
(d) divided by
(e) subtracted from
(f) multiplied by
(g) divided by
(h) multiplied by
Question: 4(ii) Give expressions for the following cases.
(e) subtracted from
(f) multiplied by
(g) divided by
(h) multiplied by
Answer:
(e) subtracted from =
(f) multiplied by
(g) divided by
(h) multiplied by
Question:5(i) Give expressions in the following cases.
(a) added to
(b) subtracted from
c) times y to which is added
(d) times y from which is subtracted
(e) is multiplied by
Answer:
(a) added to
(b) subtracted from
c) times y to which is added
(d) times y from which is subtracted
(e) is multiplied by
Question: 5(ii) Give expressions in the following cases.
(f) is multiplied by and then is added to the result
(g) is multiplied by and the result is subtracted from
(h) is multiplied by and the result is added to
Answer:
(f) is multiplied by and then is added to the result=
(g) is multiplied by and the result is subtracted from
(h) is multiplied by and the result is added to
Question: 6 (a) Form expressions using and Use not more than one number operation. Every expression must have in it.
Answer: According to given condition,
Question: 6 (b) Form expressions using and . Every expression must have in it. Use only two number operations. These should be different.
Answer: According to the given condition,
Question:1 Answer the following:
(a) Take Sarita’s present age to be years
(i) What will be her age years from now?
(ii) What was her age years back?
(iii) Sarita’s grandfather is times her age. What is the age of her grandfather?
(iv) Grandmother is years younger than grandfather. What is grandmother's age?
(v) Sarita’s father’s age is years more than times Sarita’s age. What is her father's age?
Answer: According to the given condition,
(a) (i)
(ii)
(iii) 6y
(iv)
(v)
Question: 1 (b) The length of a rectangular hall is meters less than times the breadth of the hall. What is the length, if the breadth is meters?
Answer: Breadth = b
And length = (3b4) meters
Answer: Height of box = h cm
Length of box = 5 times height = 5h cm
Breadth of box = 10 cm less than length = (5h10) cm
Question: 1 (d) Meena, Beena and Leena are climbing the steps to the hill top. Meena is at step s, Beena is 8 steps ahead and Leena steps behind. Where are Beena and Meena? The total number of steps to the hilltop is less than times what Meena has reached. Express the total number of steps using
Answer: Meena's position = s
Beena's position = 8 steps ahead = s+8
Leena's position =7 steps behind = s7
Total steps =
Answer: Speed of bus = v km\h
Distance travelled in 5 hours = 5v km
Remaining distance = 20 km
Totsl distance =
(a) A notebook costs ` .A book costs
(b) Tony puts marbles on the table. He has marbles in his box.
(c) Our class has students. The school has students.
(d) Jaggu is years old. His uncle is years old and his aunt is years old.
(e) In an arrangement of dots there are rows. Each row contains dots.
Answer:
(a) A book cost 3 times the cost of a notebook.
(b) The number of marbles in the box is 8 times marbles on the table.
(c) The total number of students in school is 20 times that in our class.
(d) Jaggu's uncle's age is 4 times the age of Jaggu. Jaggu's aunt is 3 years younger than his uncle.
(e) The total number of dots is 5 times the number of rows.
Question: 3 (a) Given Munnu’s age to be years, can you guess what may show? (Hint : Think of Munnu’s younger brother.)
Can you guess what may show? What may show?
Answer:
(a) Munnu's age = x years
Munnu’s younger brother is 2years younger than him = years
Munnu’s elder brother is 4years older than him = years
His father is 7 years more than thrice of his age =
Question: 3 (b) Given Sara’s age today to be y years. Think of her age in the future or in the past. What will the following expression indicate?
Answer:
Her age in past =
Her age in future =
Question: 3 (c) Given students in the class like football, what may show? What may show? (Hint : Think of games other than football).
Answer:
Number of students like hockey is twice the students like football, i.e.,2n
Number of students like tennis is half the students like football, i.e.,
Answer: (a) It is an equation of variable as both sides are equal. The variable is x.
Answer: (b) It is not an equation as LHS is greater than RHS.
Answer: (c) It is an equation with no variable. We may call this a numerical equation
Answer: (d) It is an equation with no variable. It is a numerical equation.
Question: 1(e) State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable.
Answer: (e) It is an equation of variable as both sides are equal. The variable is x.
Answer: (f) It is an equation of variable x.
Answer: (g) It is not an equation because LHS is less than RHS.
Answer: (h) It is an equation of variable as both sides are equal. The variable is n.
Answer: (i) It is an equation with no variable as both sides are equal.
Answer: (j) It is equation of variable p.
Answer: (k) It is an equation of varaible y.
Answer: (l) It is not an equation as LHS is less than RHS.
Answer: (m) It is not an equation as LHS is greater than RHS.
Answer: (n) It is an equation with no variable.
Answer: (o) It is an equation of variable x.
Question: 2 Complete the entries in the third column of the table.
Answer:
S. no.  Equation  Value of variable  Equ.satisfied Yes/No  Sol. of LHS 
(a)  10 y =80  y = 10  No 

(b)  10 y = 80  y = 8  Yes 

(c)  10 y = 80  y = 5  No 

(d)  4l = 20  l = 20  No 

(e)  4l = 20  l = 80  No 

(f)  4l = 20  l =5  Yes 

(g)  b + 5 =9  b = 5  No 

(h)  b + 5=9  b = 9  Yes 

(i)  b+5=9  b = 4  Yes 

(j)  h 8 =5  h =13  Yes 

(k)  h 8 =5  h = 8  No 

(l)  h 8 =5  h = 0  No 

(m)  p+3=1  p = 3  No 

(n)  p+3=1  p = 1  No 

(o)  p+3=1  p = 0  No 

(p)  p+3=1  p = 1  Yes 

(q)  p+3=1  p = 2 
(a)
(b)
(c)
(d)
(e)
(f)
Answer:
(a)
Putting given values in LHS.
m = 10 is not a solution. m = 12 is a solution.
m = 5 is not a solution. m = 15 is not a solution.
(b)
Putting given values in LHS.
n = 12 is not a solution. n = 20 is not a solution.
n = 8 is a solution. n =0 is not a solution.
(c)
Putting given values in LHS.
p =0 is not a solution. p = 10 is a solution.
p = 5 is not a solution. p = 5 is not a solution
(d)
Putting given values in LHS.
q =7 is not a solution. q = 2 is not a solution.
q = 10 is not a solution. q = 14 is a solution.
(e)
Putting given values in LHS.
r =4 is a solution. r = 4 is not a solution.
r = 8 is not a solution. r = 0 is not a solution
(f)
Putting given values in LHS.
x = 2 is a solution. x = 0 is a solution.
x = 2 is not a solution. x = 4 is not a solution
Question: 4 (a) Complete the table and by inspection of the table find the solution to the equation
Answer: (a)
m  1  2  3  4  5  6  7  8  9  10  11  12  13 
m+10  11  12  13  14  15  16  17  18  19  20  21  22  23 
At m = 6, m+10=16
Thus, m =6 is a solution.
Question: 4 (b) Complete the table and by inspection of the table, find the solution to the equation
Answer: (b)
t  3  4  5  6  7  8  9  10  11  12  13  14  15  16 
5t  15  20  25  30  35  40  45  50  55  60  65  70  75  80 
At t=7, 5t = 35
Thus, t = 7 is the solution.
Question: 4 (c) Complete the table and find the solution of the equation using the table.
Answer: (c)
z  8  9  10  11  12  13  14  15  16  17  18  19  20 

 3 

 4 

 5 

 6 


At z = 12 ,
Thus, z= 12 is a solution.
Question: 4 (d) Complete the table and find the solution to the equation
Answer: (d)
m  5  6  7  8  9  10  11  12  13  14  15 
m  7  2  1  0  1  2  3  4  5  6  7  8 
At m=10, m7 = 3
Thus, m=10 is the solution
Question:5 Solve the following riddles, you may yourself construct such riddles.
(i) Go round a square Counting every corner Thrice and no more! Add the count to me To get exactly thirty four!
(ii) For each day of the week Make an upcount from me If you make no mistake You will get twenty three!
(iii) I am a special number Take away from me a six! A whole cricket team You will still be able to fix!
(iv) Tell me who I am I shall give a pretty clue! You will get me back If you take me out of twenty two!
Answer:
(i) Square has 4 sides.
Counting every corner Thrice and no more!
Implies we go around square thrice,i.e. 12 times.
Add the count to me To get exactly thirty  four!
Let us assume the number as y, we get 34.
12+y=34
So, 22 is the number .
(ii) If 23 is number for Sunday.
Then counting up, Saturday is 22, Friday is 21, Thursday is 20.
Wednesday is 19, Tuesday is 18, Monday is 17 and Sunday is 16.
Therefore, the number considered is 16.
(iii) Let the number be x.
If we take away 6 from x, we get a cricket team.
x  6 = 11
Special number is 17.
(iv) Let the number be x.
22  x = x
22 = 2x
The number is 11.
Additional Tips and Tricks: The class 6 maths algebra often provide additional tips and tricks to simplify calculations and improve efficiency. These insights can help students save time and enhance their problemsolving abilities.
Comprehensive Coverage: The class 6 chapter 11 maths solutions cover all the major topics in the chapter, including variables, constants, algebraic expressions, like terms, coefficients, equations, and solving equations using the trial and error method. Students can be confident that they are learning all the essential concepts required for a strong foundation in algebra.
Conceptual Clarity: The chapter 11 maths class 6 explain the fundamental concepts of algebra in a clear and concise manner. They break down complex topics into simpler steps, making it easier for students to understand.
StepbyStep Approach: Each exercise in the chapter is solved stepbystep, ensuring that students can follow along and grasp the solution methodology. The solutions include detailed explanations for each step, making it easier for students to learn and apply the concepts.
Also Check
NCERT Books and NCERT Syllabus
Chapters No.  Chapters Name 
Chapter  1  Knowing Our Numbers 
Chapter  2  Whole Numbers 
Chapter  3  Playing with Numbers 
Chapter  4  Basic Geometrical Ideas 
Chapter  5  Understanding Elementary Shapes 
Chapter  6  Integers 
Chapter  7  Fractions 
Chapter  8  Decimals 
Chapter  9  Data Handling 
Chapter 10  Mensuration 
Chapter 11  Algebra 
Chapter 12  Ratio and Proportion 
Chapter 13  Symmetry 
Chapter 14  Practical Geometry 
Happy learning!!!
5 exercises are discussed in NCERT solutions for Class 6 Maths chapter 11. practice these exercises to get command in the concepts which ultimately lead to score well in the exam. Students can find detailed solutions for exercises above in this article.
Yes, Algebra is an important topic to be concentrated because it is the very basics of calculation. Also it will be used in higher Class Mathematics and Science courses. the concepts discussed in algebra questions for class 6 are foundation for algebra. Students can also study algebra books to get deeper understanding of the concepts. Also practice algebra sums for class 6 to build good command on the concepts.
An equation is written as two expressions connected by an equal sign ("="). Expressions on both sides of the equal sign are called the "left side" and "right side" of the equation.
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